Solve for $x$ and $y$ using elimination. ${-2x-3y = -32}$ ${2x-2y = 2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-5y = -30$ $\dfrac{-5y}{{-5}} = \dfrac{-30}{{-5}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-2x-3y = -32}\thinspace$ to find $x$ ${-2x - 3}{(6)}{= -32}$ $-2x-18 = -32$ $-2x-18{+18} = -32{+18}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {2x-2y = 2}\thinspace$ and get the same answer for $x$ : ${2x - 2}{(6)}{= 2}$ ${x = 7}$